This course covers lessons on propositional logic syntax and its semantics,tautology checking,analytic tableaux,formal theories,skalemization,resolution in FOL,verification of white,imperative programs and references.

COURSE DETAIL

S.No

Topic

1

Introduction

2

Propositional Logic Syntax

3

Semantics of Propositional Logic

4

Logical and Algebraic Concepts

5

Identities and Normal forms

6

Tautology Checking

7

Propositional Unsatisfiability

8

Analytic Tableaux

9

Consistency and Completeness

10

The Completeness Theorem

11

Maximally Consistent Sets

12

Formal Theories

13

Proof Theory : Hilbert-style

14

Derived Rules

15

The Hilbert System : Soundness

16

The Hilbert System :Completeness

17

Introduction to Predicate Logic

18

The Semantic of Predicate Logic

19

Subsitutions

20

Models

21

Structures and Substructures

22

First - Order Theories

23

Predicate Logic: Proof Theory (Contd..)

24

Existential Quantification

25

Normal Forms

26

Skalemization

27

Substitutions and Instantiations

28

Unification

29

Resolution in FOL

30

More on Resolution in FOL

31

Resolution : Soundness and Completeness

32

Resolution and Tableaux

33

Completeness of Tableaux Method

34

Completeness of the Hilbert System

35

First -Order Theories

36

Towards Logic Programming

37

Verification of Imperative Programs

38

Verification of WHILE Programs

39

References

Under development

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